1. Cross Reference to the Related Art    [1] Abramowitz, M, Stegun, I A. Handbook of mathematical functions, Dover Publications, NY, 1972.    [2] Astrom, K J, Hagglund, T. Automatic tuning of simple regulators with specifications on phase and amplitude margins. Automatica, 20, 645, 1984.    [3] Astrom, K J, Hagglund, T. PID controllers. 2nd ed., Instrument Society of America, NC, 1995    [4] Chiang, R, Yu, C. Monitoring Procedure for Intelligent Control: On-Line Identification of Maximum Closed-Loop Log Modulus, Ind. Eng. Chem. Research, 32, 90, 1993    [5] Friman M, Waller, K V. A two channel relay for autotuning. Ind. Eng. Chem. Research, 36, 2662-2671, 1997.    [6] Hang, C C, Astrom, K J, Wang Q G. Relay feedback auto-tuning of process controllers—a tutorial review. J. Process Control, 12, 143-162, 2002.    [7] Hang, C C, Astrom, K J, Ho, W K. Relay auto-tuning in the presence of static load disturbance. Automatica, 29, 563-564, 1993.    [8] Huang, H P, Jeng, J C, Luo, K Y. Auto-tune system using single-run relay feedback test and model-based controller design. J. Process Control, 15, 713-727, 2005.    [9] Kaya, I, Atherton, D P. Parameter estimation from relay autotuning with asymmetric limit cycle data. J. Process Control, 11, 429-439, 2001.    [10] Kim, Y H. P I Controller Tuning Using Modified Relay Feedback Method, J. Chem. Eng. Japan, 28, 118, 1995.    [11] Kreyszig, E. Advanced engineering mathematics. 8th ed., New York, Wiley, 1999.    [12] Luyben, W L. Getting more information from relay feedback tests. Ind. Eng. Chem. Research, 40, 4391, 2001.    [13] Ma, M D, Zhu, X J. A simple auto-tuner in frequency domain. Comp. Chem. Eng., 2006.    [14] Panda, R C, Yu, C C. Analytic expressions for relay feedback responses. J. Process Control, 13, 48, 2003.    [15] Panda, R C, Yu, C C. Shape factor of relay response curves and its use in autotuning. J. Process Control, 15, 893-906, 2005.    [16] Shen, S H, Wu, J S, Yu, C C. Use of biased relay feedback method for system identification. AIChE J., 42, 1174-1180, 1996a.    [17] Shen, S H, Wu, J S, Yu, C C. Autotune identification under load disturbance. Ind. Eng. Chem. Research, 35, 1642-1651, 1996b.    [18] Sung, S W, Park, J H, Lee, I. Modified relay feedback method. Ind. Eng. Chem. Research, 34, 4133-4135, 1995.    [19] Sung, S W, Lee, I. Enhanced relay feedback method, Ind. Eng. Chem. Research, 36, 5526, 1997.    [20] Sung, S W, Lee, J., Lee, D H, Han, J H, Park, Y S. A Two-Channel Relay Feedback Method under Static Disturbances, Ind. Eng. Chem. Research, 45, 4071, 2006.    [21] Sung, S W, Lee, J. Relay feedback method under large static disturbances. Automatica, 42, 353-356, 2006.    [22] Sung, S W, O, J, Lee, I, Lee, J, Yi, S H. Automatic Tuning of PID Controller using Second-Order Plus Time Delay Model, J. Chem. Eng. Japan, 29, 990, 1996.    [23] Tan, K K, Lee, T H, Huang, S, Chua, K Y, Ferdous, R. Improved critical point estimation using a preload relay. J. Process Control, 2005.    [24] Tan, K K, Lee, T H, Wang, Q G. Enhanced automatic tuning procedure for process control of PI/PID controllers, AIChE J., 42, 2555, 1996.    [25] Wang, Q G, Hang, C C, Bi, Q. Process frequency response estimation from relay feedback. Control Eng. Practice, 5, 1293-1302, 1997a.    [26] Wang, Q G, Hang, C C, Zou, B. Low order modeling from relay feedback. Ind. Eng. Chem. Research, 36, 375, 1997b.    [27] Yu, C C. Autotuning of PID controllers: A relay feedback approach. 2nd ed. Springer, London, 2006.
2. Field of the Invention
The present invention relates to an autotuning method for a PID (Proportional Integral Derivative) controller, and in particular to an autotuning method using an integral of a relay feedback response in which an ultimate data and a frequency model of a process can be reliably obtained by integrating a relay feedback signal and removing a lot of harmonics.
3. Description of the Related Art
PID controller has been widely used in various industrial facilities due to its simple structure and excellent control performance. The PID controller may solely use a proportional control, an integral control or a derivative control or may combine and use at least two controls of the above methods.
The relay feedback methods for autotuning of a PID controller have been widely used. In the conventional relay feedback methods, a frequency model of a process is computed using an oscillation period and an oscillation magnitude of input and output responses. The above method will be described in details as follows.
Since [2] Astrom and Hagglund (1984) introduced the autotuning method, which used the relay feedback test, many variations have been proposed for autotuning of PID controllers ([3] Astrom and Hagglund, 1995; Hang et al., 2002; Yu, 2006). Several methods such as a saturation relay ([27] Yu, 2006), relay with a P control preload ([23] Tan et al., 2005) and a two level relay ([28] Sung et al., 1995) were introduced to obtain more accurate ultimate data of the process by suppressing the effects of the high order harmonic terms. To obtain a Nyquist point other than the ultimate point, a relay with hysteresis or a dynamic element such as time delay has been used ([3] Astrom and Hagglund, 1995; [10] Kim, 1995; [24] Tan et al., 1996; [4] Chiang and Yu, 1993). Recently, a two channel relay has been proposed to obtain a Nyquist point information corresponding to a given phase angle ([5] Friman and Waller, 1997; [20] Sung et al., 2006). Methods to reject unknown load disturbances and restore symmetric relay oscillations have been available ([7] Hang et al., 1993; [17] Shen et al, 1996b; [21] Sung and Lee, 2006). A biased relay has been used to obtain the process steady state gain as well as the ultimate data ([16] Shen et al., 1996a) from only one relay test. [8] Huang et al. (2005) used the integral of the relay transient to obtain the steady state gain of the process.
Many Nyquist points of the process dynamics can be extracted from only one relay experiment by applying the FFT (fast Fourier transformation) technique to the whole transient responses from the start to the final cyclic steady-state part of the relay responses ([25] Wang et al., 1997a). However, the computations are somewhat complex and the complete transient responses must be stored. For the same purpose, Laplace transformation of a periodic function has been used to obtain many frequency responses from one relay test ([13] Ma and Zhu, 2006).
The shape factor (Luyben, 2001) has been used to extract a three-parameter model from the cyclic steady state part of the relay response. Several authors ([9] Kaya and Atherton, 2001; [14] Panda and Yu, 2003) derived exact expressions relating the parameters of the FOPTD process to the measured data of the relay response. They used the analytic expressions to extract parameters of the FOPTD model. However, the methods based only on the cyclic steady state data cannot provide acceptable robustness for uncertainty such as process/model mismatches and nonlinearity. They may provide poor model parameter estimates such as negative gain when the model structure is different from that of the process ([15] Panda and Yu, 2005). The second order plus time delay (SOPTD) model can be also extracted from the cyclic steady state part of the relay response using analytic equations. However, as in the FOPTD model case, the method is also not robust. A relay experiment with a subsequent P control experiment or another relay feedback test can be used to obtain an SOPTD model robustly ([22] Sung et al., 1996; [19] Sung and Lee, 1997).